Question

Define Arithmetic Progression (A.P.).

Answer 1

A sequence is called an arithmetic progression, if the difference of two consecutive term is the same always.

i.e. a_n – a_n–1 = d, (constant), n ∈ N.

Here d is called the common difference (If d= 0 sequence is a constant sequence. if d>0 the sequence is increasing; if d<0,the sequence is decreasing)

n^th term of an A.P = a+(n–1)d

n^th term from end of an A.P = a_n + (n – 1) (–d)

where a_n is the last term and d, the common difference of the A.P.